- #1

- 128

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In deriving the WKB approximation the wave function is written as

[tex]

\psi \left( x \right) = exp\left[ i S\left( x \right) \right ]

[/tex]

Now, in some of the deriviations I've seen, the function S(x) is expanded as a power series in [tex]\hbar[/tex] as

[tex]

S(x) = S_0(x) + \hbar S_1(x) + \frac{\hbar}{2} S_2(x) ...

[/tex]

I don't really understand this. It's something like [tex]S_0[/tex] being the classical result and, the next term being a first order quantum correction and so on. But why do you choose to expand in powers of [tex]\hbar[/tex]? Can somebody explain to me what this is all about?

Thanks in advance

René